Question

bc || ad
reason:
given
∠bca ≅ ∠dac
reason:
given
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given
reflexive property
vertical angles are
congruent
all right angles are
congruent
an angle bisector divides an
angle into two congruent
angles
parallel lines cut by a
transversal form congruent
alternate interior angles

Explanation:

Step1: Analyze the relationship between lines and angles

We know that \( \overline{BC}\parallel\overline{AD}\), and \( \angle BCA\) and \( \angle DAC\) are angles formed by a transversal intersecting these parallel lines.

Step2: Recall the property of parallel lines and transversals

When parallel lines are cut by a transversal, alternate - interior angles are congruent. Here, \( \overline{AC}\) is the transversal for parallel lines \( \overline{BC}\) and \( \overline{AD}\). So, \( \angle BCA\) and \( \angle DAC\) are alternate - interior angles.

Answer:

Parallel lines cut by a transversal form congruent alternate interior angles.